LMFDB - Embedded newform 2001.2.a.m.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2001,2,Mod(1,2001)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2001, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("2001.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2001 = 3 \cdot 23 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2001.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$15.9780654445$
Analytic rank:	$1$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 2 x^{13} - 18 x^{12} + 34 x^{11} + 124 x^{10} - 216 x^{9} - 420 x^{8} + 647 x^{7} + 750 x^{6} + \cdots - 64 $ x^14 - 2x^13 - 18x^12 + 34x^11 + 124x^10 - 216x^9 - 420x^8 + 647x^7 + 750x^6 - 939x^5 - 717x^4 + 604x^3 + 352x^2 - 128*x - 64
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$1.57408$ of defining polynomial
Character	$\chi$	$=$	2001.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.57408 q^{2} -1.00000 q^{3} +0.477741 q^{4} +0.564555 q^{5} +1.57408 q^{6} -3.58089 q^{7} +2.39616 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.57408 q^{2} -1.00000 q^{3} +0.477741 q^{4} +0.564555 q^{5} +1.57408 q^{6} -3.58089 q^{7} +2.39616 q^{8} +1.00000 q^{9} -0.888657 q^{10} -0.304207 q^{11} -0.477741 q^{12} -3.30762 q^{13} +5.63662 q^{14} -0.564555 q^{15} -4.72725 q^{16} +5.79972 q^{17} -1.57408 q^{18} +3.49580 q^{19} +0.269711 q^{20} +3.58089 q^{21} +0.478847 q^{22} -1.00000 q^{23} -2.39616 q^{24} -4.68128 q^{25} +5.20647 q^{26} -1.00000 q^{27} -1.71074 q^{28} -1.00000 q^{29} +0.888657 q^{30} +2.40570 q^{31} +2.64875 q^{32} +0.304207 q^{33} -9.12925 q^{34} -2.02161 q^{35} +0.477741 q^{36} +6.97568 q^{37} -5.50268 q^{38} +3.30762 q^{39} +1.35277 q^{40} +0.962917 q^{41} -5.63662 q^{42} +10.6463 q^{43} -0.145332 q^{44} +0.564555 q^{45} +1.57408 q^{46} -7.76764 q^{47} +4.72725 q^{48} +5.82279 q^{49} +7.36872 q^{50} -5.79972 q^{51} -1.58018 q^{52} +6.81129 q^{53} +1.57408 q^{54} -0.171741 q^{55} -8.58041 q^{56} -3.49580 q^{57} +1.57408 q^{58} -10.6109 q^{59} -0.269711 q^{60} -9.74982 q^{61} -3.78677 q^{62} -3.58089 q^{63} +5.28513 q^{64} -1.86733 q^{65} -0.478847 q^{66} +0.430036 q^{67} +2.77076 q^{68} +1.00000 q^{69} +3.18218 q^{70} -7.39631 q^{71} +2.39616 q^{72} +9.36770 q^{73} -10.9803 q^{74} +4.68128 q^{75} +1.67008 q^{76} +1.08933 q^{77} -5.20647 q^{78} +1.31647 q^{79} -2.66879 q^{80} +1.00000 q^{81} -1.51571 q^{82} +0.543719 q^{83} +1.71074 q^{84} +3.27426 q^{85} -16.7581 q^{86} +1.00000 q^{87} -0.728929 q^{88} +10.0393 q^{89} -0.888657 q^{90} +11.8442 q^{91} -0.477741 q^{92} -2.40570 q^{93} +12.2269 q^{94} +1.97357 q^{95} -2.64875 q^{96} +4.33932 q^{97} -9.16556 q^{98} -0.304207 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 2 q^{2} - 14 q^{3} + 12 q^{4} - 3 q^{5} + 2 q^{6} - 3 q^{7} - 6 q^{8} + 14 q^{9}+O(q^{10}) $ 14 * q - 2 * q^2 - 14 * q^3 + 12 * q^4 - 3 * q^5 + 2 * q^6 - 3 * q^7 - 6 * q^8 + 14 * q^9	\( 14 q - 2 q^{2} - 14 q^{3} + 12 q^{4} - 3 q^{5} + 2 q^{6} - 3 q^{7} - 6 q^{8} + 14 q^{9} - 5 q^{10} - 12 q^{11} - 12 q^{12} + 13 q^{13} - 9 q^{14} + 3 q^{15} - 14 q^{17} - 2 q^{18} - 9 q^{19} - 2 q^{20} + 3 q^{21} - 9 q^{22} - 14 q^{23} + 6 q^{24} + 13 q^{25} - 16 q^{26} - 14 q^{27} + 3 q^{28} - 14 q^{29} + 5 q^{30} - 28 q^{31} - 4 q^{32} + 12 q^{33} + 14 q^{34} - 9 q^{35} + 12 q^{36} - 12 q^{37} + 2 q^{38} - 13 q^{39} - 20 q^{40} - 25 q^{41} + 9 q^{42} + 5 q^{43} - 37 q^{44} - 3 q^{45} + 2 q^{46} - 17 q^{47} + 17 q^{49} - 44 q^{50} + 14 q^{51} + 25 q^{52} - 17 q^{53} + 2 q^{54} + q^{55} - 54 q^{56} + 9 q^{57} + 2 q^{58} - 18 q^{59} + 2 q^{60} - 13 q^{61} - 8 q^{62} - 3 q^{63} + 20 q^{64} - 16 q^{65} + 9 q^{66} + 2 q^{67} - 19 q^{68} + 14 q^{69} + 14 q^{70} - 55 q^{71} - 6 q^{72} + 19 q^{73} + 4 q^{74} - 13 q^{75} - 32 q^{76} - 19 q^{77} + 16 q^{78} - 68 q^{79} - 2 q^{80} + 14 q^{81} - 12 q^{82} - 21 q^{83} - 3 q^{84} + 16 q^{85} - 22 q^{86} + 14 q^{87} - 25 q^{88} - 17 q^{89} - 5 q^{90} - 30 q^{91} - 12 q^{92} + 28 q^{93} + 16 q^{94} - 55 q^{95} + 4 q^{96} + 25 q^{97} - 31 q^{98} - 12 q^{99}+O(q^{100}) \) 14 * q - 2 * q^2 - 14 * q^3 + 12 * q^4 - 3 * q^5 + 2 * q^6 - 3 * q^7 - 6 * q^8 + 14 * q^9 - 5 * q^10 - 12 * q^11 - 12 * q^12 + 13 * q^13 - 9 * q^14 + 3 * q^15 - 14 * q^17 - 2 * q^18 - 9 * q^19 - 2 * q^20 + 3 * q^21 - 9 * q^22 - 14 * q^23 + 6 * q^24 + 13 * q^25 - 16 * q^26 - 14 * q^27 + 3 * q^28 - 14 * q^29 + 5 * q^30 - 28 * q^31 - 4 * q^32 + 12 * q^33 + 14 * q^34 - 9 * q^35 + 12 * q^36 - 12 * q^37 + 2 * q^38 - 13 * q^39 - 20 * q^40 - 25 * q^41 + 9 * q^42 + 5 * q^43 - 37 * q^44 - 3 * q^45 + 2 * q^46 - 17 * q^47 + 17 * q^49 - 44 * q^50 + 14 * q^51 + 25 * q^52 - 17 * q^53 + 2 * q^54 + q^55 - 54 * q^56 + 9 * q^57 + 2 * q^58 - 18 * q^59 + 2 * q^60 - 13 * q^61 - 8 * q^62 - 3 * q^63 + 20 * q^64 - 16 * q^65 + 9 * q^66 + 2 * q^67 - 19 * q^68 + 14 * q^69 + 14 * q^70 - 55 * q^71 - 6 * q^72 + 19 * q^73 + 4 * q^74 - 13 * q^75 - 32 * q^76 - 19 * q^77 + 16 * q^78 - 68 * q^79 - 2 * q^80 + 14 * q^81 - 12 * q^82 - 21 * q^83 - 3 * q^84 + 16 * q^85 - 22 * q^86 + 14 * q^87 - 25 * q^88 - 17 * q^89 - 5 * q^90 - 30 * q^91 - 12 * q^92 + 28 * q^93 + 16 * q^94 - 55 * q^95 + 4 * q^96 + 25 * q^97 - 31 * q^98 - 12 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.57408	−1.11305	−0.556523	−	0.830832i	$-0.687865\pi$
$2$	−1.57408	−1.11305	−0.556523	+	0.830832i	$0.687865\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	0.477741	0.238870
$5$	0.564555	0.252477	0.126238	−	0.992000i	$-0.459710\pi$
$5$	0.564555	0.252477	0.126238	+	0.992000i	$0.459710\pi$
$6$	1.57408	0.642617
$7$	−3.58089	−1.35345	−0.676725	−	0.736236i	$-0.736601\pi$
$7$	−3.58089	−1.35345	−0.676725	+	0.736236i	$0.736601\pi$
$8$	2.39616	0.847172
$9$	1.00000	0.333333
$10$	−0.888657	−0.281018
$11$	−0.304207	−0.0917218	−0.0458609	−	0.998948i	$-0.514603\pi$
$11$	−0.304207	−0.0917218	−0.0458609	+	0.998948i	$0.514603\pi$
$12$	−0.477741	−0.137912
$13$	−3.30762	−0.917368	−0.458684	−	0.888599i	$-0.651679\pi$
$13$	−3.30762	−0.917368	−0.458684	+	0.888599i	$0.651679\pi$
$14$	5.63662	1.50645
$15$	−0.564555	−0.145767
$16$	−4.72725	−1.18181
$17$	5.79972	1.40664	0.703320	−	0.710873i	$-0.251700\pi$
$17$	5.79972	1.40664	0.703320	+	0.710873i	$0.251700\pi$
$18$	−1.57408	−0.371015
$19$	3.49580	0.801991	0.400996	−	0.916080i	$-0.368664\pi$
$19$	3.49580	0.801991	0.400996	+	0.916080i	$0.368664\pi$
$20$	0.269711	0.0603092
$21$	3.58089	0.781415
$22$	0.478847	0.102090
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−2.39616	−0.489115
$25$	−4.68128	−0.936256
$26$	5.20647	1.02107
$27$	−1.00000	−0.192450
$28$	−1.71074	−0.323299
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	0.888657	0.162246
$31$	2.40570	0.432076	0.216038	−	0.976385i	$-0.430686\pi$
$31$	2.40570	0.432076	0.216038	+	0.976385i	$0.430686\pi$
$32$	2.64875	0.468238
$33$	0.304207	0.0529556
$34$	−9.12925	−1.56565
$35$	−2.02161	−0.341714
$36$	0.477741	0.0796234
$37$	6.97568	1.14679	0.573397	−	0.819278i	$-0.305625\pi$
$37$	6.97568	1.14679	0.573397	+	0.819278i	$0.305625\pi$
$38$	−5.50268	−0.892653
$39$	3.30762	0.529643
$40$	1.35277	0.213891
$41$	0.962917	0.150382	0.0751912	−	0.997169i	$-0.476043\pi$
$41$	0.962917	0.150382	0.0751912	+	0.997169i	$0.476043\pi$
$42$	−5.63662	−0.869750
$43$	10.6463	1.62354	0.811771	−	0.583976i	$-0.198504\pi$
$43$	10.6463	1.62354	0.811771	+	0.583976i	$0.198504\pi$
$44$	−0.145332	−0.0219096
$45$	0.564555	0.0841589
$46$	1.57408	0.232086
$47$	−7.76764	−1.13303	−0.566514	−	0.824052i	$-0.691708\pi$
$47$	−7.76764	−1.13303	−0.566514	+	0.824052i	$0.691708\pi$
$48$	4.72725	0.682319
$49$	5.82279	0.831827
$50$	7.36872	1.04210
$51$	−5.79972	−0.812124
$52$	−1.58018	−0.219132
$53$	6.81129	0.935603	0.467802	−	0.883833i	$-0.345046\pi$
$53$	6.81129	0.935603	0.467802	+	0.883833i	$0.345046\pi$
$54$	1.57408	0.214206
$55$	−0.171741	−0.0231576
$56$	−8.58041	−1.14660
$57$	−3.49580	−0.463030
$58$	1.57408	0.206687
$59$	−10.6109	−1.38143	−0.690713	−	0.723129i	$-0.742703\pi$
$59$	−10.6109	−1.38143	−0.690713	+	0.723129i	$0.742703\pi$
$60$	−0.269711	−0.0348195
$61$	−9.74982	−1.24834	−0.624168	−	0.781290i	$-0.714562\pi$
$61$	−9.74982	−1.24834	−0.624168	+	0.781290i	$0.714562\pi$
$62$	−3.78677	−0.480921
$63$	−3.58089	−0.451150
$64$	5.28513	0.660641
$65$	−1.86733	−0.231614
$66$	−0.478847	−0.0589420
$67$	0.430036	0.0525372	0.0262686	−	0.999655i	$-0.491637\pi$
$67$	0.430036	0.0525372	0.0262686	+	0.999655i	$0.491637\pi$
$68$	2.77076	0.336004
$69$	1.00000	0.120386
$70$	3.18218	0.380344
$71$	−7.39631	−0.877780	−0.438890	−	0.898541i	$-0.644628\pi$
$71$	−7.39631	−0.877780	−0.438890	+	0.898541i	$0.644628\pi$
$72$	2.39616	0.282391
$73$	9.36770	1.09641	0.548203	−	0.836345i	$-0.315312\pi$
$73$	9.36770	1.09641	0.548203	+	0.836345i	$0.315312\pi$
$74$	−10.9803	−1.27643
$75$	4.68128	0.540547
$76$	1.67008	0.191572
$77$	1.08933	0.124141
$78$	−5.20647	−0.589517
$79$	1.31647	0.148114	0.0740569	−	0.997254i	$-0.476405\pi$
$79$	1.31647	0.148114	0.0740569	+	0.997254i	$0.476405\pi$
$80$	−2.66879	−0.298380
$81$	1.00000	0.111111
$82$	−1.51571	−0.167382
$83$	0.543719	0.0596809	0.0298405	−	0.999555i	$-0.490500\pi$
$83$	0.543719	0.0596809	0.0298405	+	0.999555i	$0.490500\pi$
$84$	1.71074	0.186657
$85$	3.27426	0.355144
$86$	−16.7581	−1.80708
$87$	1.00000	0.107211
$88$	−0.728929	−0.0777041
$89$	10.0393	1.06416	0.532082	−	0.846693i	$-0.321410\pi$
$89$	10.0393	1.06416	0.532082	+	0.846693i	$0.321410\pi$
$90$	−0.888657	−0.0936726
$91$	11.8442	1.24161
$92$	−0.477741	−0.0498079
$93$	−2.40570	−0.249459
$94$	12.2269	1.26111
$95$	1.97357	0.202484
$96$	−2.64875	−0.270337
$97$	4.33932	0.440591	0.220295	−	0.975433i	$-0.429298\pi$
$97$	4.33932	0.440591	0.220295	+	0.975433i	$0.429298\pi$
$98$	−9.16556	−0.925861
$99$	−0.304207	−0.0305739
$100$	−2.23644	−0.223644
$101$	2.65520	0.264202	0.132101	−	0.991236i	$-0.457828\pi$
$101$	2.65520	0.264202	0.132101	+	0.991236i	$0.457828\pi$
$102$	9.12925	0.903931
$103$	9.17708	0.904245	0.452122	−	0.891956i	$-0.350667\pi$
$103$	9.17708	0.904245	0.452122	+	0.891956i	$0.350667\pi$
$104$	−7.92560	−0.777169
$105$	2.02161	0.197289
$106$	−10.7215	−1.04137
$107$	−1.49460	−0.144489	−0.0722443	−	0.997387i	$-0.523016\pi$
$107$	−1.49460	−0.144489	−0.0722443	+	0.997387i	$0.523016\pi$
$108$	−0.477741	−0.0459706
$109$	−14.2657	−1.36640	−0.683201	−	0.730230i	$-0.739413\pi$
$109$	−14.2657	−1.36640	−0.683201	+	0.730230i	$0.739413\pi$
$110$	0.270335	0.0257755
$111$	−6.97568	−0.662102
$112$	16.9278	1.59952
$113$	−3.04388	−0.286344	−0.143172	−	0.989698i	$-0.545730\pi$
$113$	−3.04388	−0.286344	−0.143172	+	0.989698i	$0.545730\pi$
$114$	5.50268	0.515373
$115$	−0.564555	−0.0526450
$116$	−0.477741	−0.0443571
$117$	−3.30762	−0.305789
$118$	16.7025	1.53759
$119$	−20.7682	−1.90382
$120$	−1.35277	−0.123490
$121$	−10.9075	−0.991587
$122$	15.3470	1.38946
$123$	−0.962917	−0.0868233
$124$	1.14930	0.103210
$125$	−5.46561	−0.488859
$126$	5.63662	0.502150
$127$	−6.50048	−0.576824	−0.288412	−	0.957506i	$-0.593127\pi$
$127$	−6.50048	−0.576824	−0.288412	+	0.957506i	$0.593127\pi$
$128$	−13.6167	−1.20356
$129$	−10.6463	−0.937352
$130$	2.93934	0.257797
$131$	−12.3389	−1.07805	−0.539026	−	0.842289i	$-0.681207\pi$
$131$	−12.3389	−1.07805	−0.539026	+	0.842289i	$0.681207\pi$
$132$	0.145332	0.0126495
$133$	−12.5181	−1.08546
$134$	−0.676913	−0.0584763
$135$	−0.564555	−0.0485891
$136$	13.8971	1.19167
$137$	−2.84962	−0.243460	−0.121730	−	0.992563i	$-0.538844\pi$
$137$	−2.84962	−0.243460	−0.121730	+	0.992563i	$0.538844\pi$
$138$	−1.57408	−0.133995
$139$	−21.0327	−1.78397	−0.891986	−	0.452063i	$-0.850688\pi$
$139$	−21.0327	−1.78397	−0.891986	+	0.452063i	$0.850688\pi$
$140$	−0.965805	−0.0816254
$141$	7.76764	0.654154
$142$	11.6424	0.977009
$143$	1.00620	0.0841426
$144$	−4.72725	−0.393937
$145$	−0.564555	−0.0468837
$146$	−14.7455	−1.22035
$147$	−5.82279	−0.480255
$148$	3.33256	0.273935
$149$	−5.23672	−0.429009	−0.214505	−	0.976723i	$-0.568814\pi$
$149$	−5.23672	−0.429009	−0.214505	+	0.976723i	$0.568814\pi$
$150$	−7.36872	−0.601654
$151$	−5.82423	−0.473969	−0.236985	−	0.971513i	$-0.576159\pi$
$151$	−5.82423	−0.473969	−0.236985	+	0.971513i	$0.576159\pi$
$152$	8.37651	0.679425
$153$	5.79972	0.468880
$154$	−1.71470	−0.138174
$155$	1.35815	0.109089
$156$	1.58018	0.126516
$157$	−0.208492	−0.0166394	−0.00831972	−	0.999965i	$-0.502648\pi$
$157$	−0.208492	−0.0166394	−0.00831972	+	0.999965i	$0.502648\pi$
$158$	−2.07223	−0.164858
$159$	−6.81129	−0.540171
$160$	1.49537	0.118219
$161$	3.58089	0.282214
$162$	−1.57408	−0.123672
$163$	−4.45218	−0.348722	−0.174361	−	0.984682i	$-0.555786\pi$
$163$	−4.45218	−0.348722	−0.174361	+	0.984682i	$0.555786\pi$
$164$	0.460025	0.0359219
$165$	0.171741	0.0133700
$166$	−0.855860	−0.0664276
$167$	−13.1436	−1.01708	−0.508542	−	0.861037i	$-0.669815\pi$
$167$	−13.1436	−1.01708	−0.508542	+	0.861037i	$0.669815\pi$
$168$	8.58041	0.661993
$169$	−2.05966	−0.158435
$170$	−5.15396	−0.395291
$171$	3.49580	0.267330
$172$	5.08616	0.387816
$173$	−10.6235	−0.807690	−0.403845	−	0.914827i	$-0.632326\pi$
$173$	−10.6235	−0.807690	−0.403845	+	0.914827i	$0.632326\pi$
$174$	−1.57408	−0.119331
$175$	16.7631	1.26717
$176$	1.43806	0.108398
$177$	10.6109	0.797567
$178$	−15.8027	−1.18446
$179$	−8.73207	−0.652666	−0.326333	−	0.945255i	$-0.605813\pi$
$179$	−8.73207	−0.652666	−0.326333	+	0.945255i	$0.605813\pi$
$180$	0.269711	0.0201031
$181$	3.19822	0.237722	0.118861	−	0.992911i	$-0.462076\pi$
$181$	3.19822	0.237722	0.118861	+	0.992911i	$0.462076\pi$
$182$	−18.6438	−1.38197
$183$	9.74982	0.720727
$184$	−2.39616	−0.176648
$185$	3.93815	0.289539
$186$	3.78677	0.277660
$187$	−1.76431	−0.129019
$188$	−3.71092	−0.270647
$189$	3.58089	0.260472
$190$	−3.10657	−0.225374
$191$	0.948797	0.0686526	0.0343263	−	0.999411i	$-0.489071\pi$
$191$	0.948797	0.0686526	0.0343263	+	0.999411i	$0.489071\pi$
$192$	−5.28513	−0.381422
$193$	1.42893	0.102856	0.0514282	−	0.998677i	$-0.483623\pi$
$193$	1.42893	0.102856	0.0514282	+	0.998677i	$0.483623\pi$
$194$	−6.83045	−0.490398
$195$	1.86733	0.133722
$196$	2.78178	0.198699
$197$	−5.74579	−0.409371	−0.204685	−	0.978828i	$-0.565617\pi$
$197$	−5.74579	−0.409371	−0.204685	+	0.978828i	$0.565617\pi$
$198$	0.478847	0.0340302
$199$	−10.2525	−0.726783	−0.363392	−	0.931636i	$-0.618381\pi$
$199$	−10.2525	−0.726783	−0.363392	+	0.931636i	$0.618381\pi$
$200$	−11.2171	−0.793170
$201$	−0.430036	−0.0303324
$202$	−4.17950	−0.294069
$203$	3.58089	0.251329
$204$	−2.77076	−0.193992
$205$	0.543620	0.0379680
$206$	−14.4455	−1.00647
$207$	−1.00000	−0.0695048
$208$	15.6359	1.08416
$209$	−1.06345	−0.0735601
$210$	−3.18218	−0.219592
$211$	−9.12656	−0.628298	−0.314149	−	0.949374i	$-0.601719\pi$
$211$	−9.12656	−0.628298	−0.314149	+	0.949374i	$0.601719\pi$
$212$	3.25403	0.223488
$213$	7.39631	0.506786
$214$	2.35263	0.160822
$215$	6.01040	0.409906
$216$	−2.39616	−0.163038
$217$	−8.61455	−0.584794
$218$	22.4553	1.52087
$219$	−9.36770	−0.633010
$220$	−0.0820478	−0.00553166
$221$	−19.1833	−1.29041
$222$	10.9803	0.736949
$223$	−14.8570	−0.994896	−0.497448	−	0.867494i	$-0.665729\pi$
$223$	−14.8570	−0.994896	−0.497448	+	0.867494i	$0.665729\pi$
$224$	−9.48490	−0.633736
$225$	−4.68128	−0.312085
$226$	4.79133	0.318714
$227$	−9.64893	−0.640422	−0.320211	−	0.947346i	$-0.603754\pi$
$227$	−9.64893	−0.640422	−0.320211	+	0.947346i	$0.603754\pi$
$228$	−1.67008	−0.110604
$229$	18.8161	1.24340	0.621700	−	0.783255i	$-0.286442\pi$
$229$	18.8161	1.24340	0.621700	+	0.783255i	$0.286442\pi$
$230$	0.888657	0.0585963
$231$	−1.08933	−0.0716727
$232$	−2.39616	−0.157316
$233$	−23.8649	−1.56344	−0.781721	−	0.623628i	$-0.785658\pi$
$233$	−23.8649	−1.56344	−0.781721	+	0.623628i	$0.785658\pi$
$234$	5.20647	0.340358
$235$	−4.38526	−0.286063
$236$	−5.06927	−0.329982
$237$	−1.31647	−0.0855136
$238$	32.6909	2.11903
$239$	−5.00870	−0.323986	−0.161993	−	0.986792i	$-0.551792\pi$
$239$	−5.00870	−0.323986	−0.161993	+	0.986792i	$0.551792\pi$
$240$	2.66879	0.172270
$241$	18.1557	1.16951	0.584757	−	0.811209i	$-0.301190\pi$
$241$	18.1557	1.16951	0.584757	+	0.811209i	$0.301190\pi$
$242$	17.1693	1.10368
$243$	−1.00000	−0.0641500
$244$	−4.65788	−0.298190
$245$	3.28728	0.210017
$246$	1.51571	0.0966383
$247$	−11.5628	−0.735721
$248$	5.76445	0.366043
$249$	−0.543719	−0.0344568
$250$	8.60333	0.544123
$251$	−5.36176	−0.338431	−0.169216	−	0.985579i	$-0.554123\pi$
$251$	−5.36176	−0.338431	−0.169216	+	0.985579i	$0.554123\pi$
$252$	−1.71074	−0.107766
$253$	0.304207	0.0191253
$254$	10.2323	0.642032
$255$	−3.27426	−0.205042
$256$	10.8636	0.678977
$257$	23.6911	1.47781	0.738904	−	0.673810i	$-0.235343\pi$
$257$	23.6911	1.47781	0.738904	+	0.673810i	$0.235343\pi$
$258$	16.7581	1.04332
$259$	−24.9791	−1.55213
$260$	−0.892100	−0.0553257
$261$	−1.00000	−0.0618984
$262$	19.4224	1.19992
$263$	−11.2840	−0.695803	−0.347901	−	0.937531i	$-0.613106\pi$
$263$	−11.2840	−0.695803	−0.347901	+	0.937531i	$0.613106\pi$
$264$	0.728929	0.0448625
$265$	3.84535	0.236218
$266$	19.7045	1.20816
$267$	−10.0393	−0.614395
$268$	0.205446	0.0125496
$269$	−2.75812	−0.168166	−0.0840829	−	0.996459i	$-0.526796\pi$
$269$	−2.75812	−0.168166	−0.0840829	+	0.996459i	$0.526796\pi$
$270$	0.888657	0.0540819
$271$	−19.1922	−1.16584	−0.582922	−	0.812528i	$-0.698091\pi$
$271$	−19.1922	−1.16584	−0.582922	+	0.812528i	$0.698091\pi$
$272$	−27.4167	−1.66238
$273$	−11.8442	−0.716845
$274$	4.48555	0.270982
$275$	1.42408	0.0858750
$276$	0.477741	0.0287566
$277$	14.6988	0.883167	0.441583	−	0.897220i	$-0.354417\pi$
$277$	14.6988	0.883167	0.441583	+	0.897220i	$0.354417\pi$
$278$	33.1073	1.98564
$279$	2.40570	0.144025
$280$	−4.84411	−0.289491
$281$	1.95511	0.116632	0.0583159	−	0.998298i	$-0.481427\pi$
$281$	1.95511	0.116632	0.0583159	+	0.998298i	$0.481427\pi$
$282$	−12.2269	−0.728103
$283$	−3.99785	−0.237648	−0.118824	−	0.992915i	$-0.537912\pi$
$283$	−3.99785	−0.237648	−0.118824	+	0.992915i	$0.537912\pi$
$284$	−3.53351	−0.209676
$285$	−1.97357	−0.116904
$286$	−1.58384	−0.0936546
$287$	−3.44810	−0.203535
$288$	2.64875	0.156079
$289$	16.6368	0.978636
$290$	0.888657	0.0521837
$291$	−4.33932	−0.254375
$292$	4.47533	0.261899
$293$	−22.3404	−1.30514	−0.652569	−	0.757729i	$-0.726309\pi$
$293$	−22.3404	−1.30514	−0.652569	+	0.757729i	$0.726309\pi$
$294$	9.16556	0.534546
$295$	−5.99045	−0.348778
$296$	16.7149	0.971532
$297$	0.304207	0.0176519
$298$	8.24304	0.477507
$299$	3.30762	0.191285
$300$	2.23644	0.129121
$301$	−38.1232	−2.19738
$302$	9.16783	0.527549
$303$	−2.65520	−0.152537
$304$	−16.5255	−0.947802
$305$	−5.50431	−0.315176
$306$	−9.12925	−0.521885
$307$	2.18004	0.124421	0.0622107	−	0.998063i	$-0.480185\pi$
$307$	2.18004	0.124421	0.0622107	+	0.998063i	$0.480185\pi$
$308$	0.520418	0.0296535
$309$	−9.17708	−0.522066
$310$	−2.13784	−0.121421
$311$	−32.7933	−1.85954	−0.929770	−	0.368141i	$-0.879994\pi$
$311$	−32.7933	−1.85954	−0.929770	+	0.368141i	$0.879994\pi$
$312$	7.92560	0.448699
$313$	−17.3235	−0.979183	−0.489591	−	0.871952i	$-0.662854\pi$
$313$	−17.3235	−0.979183	−0.489591	+	0.871952i	$0.662854\pi$
$314$	0.328183	0.0185205
$315$	−2.02161	−0.113905
$316$	0.628929	0.0353800
$317$	−0.0184851	−0.00103822	−0.000519112	−	1.00000i	$-0.500165\pi$
$317$	−0.0184851	−0.00103822	−0.000519112		1.00000i	$0.500165\pi$
$318$	10.7215	0.601235
$319$	0.304207	0.0170323
$320$	2.98375	0.166797
$321$	1.49460	0.0834205
$322$	−5.63662	−0.314117
$323$	20.2747	1.12811
$324$	0.477741	0.0265411
$325$	15.4839	0.858891
$326$	7.00811	0.388143
$327$	14.2657	0.788893
$328$	2.30731	0.127400
$329$	27.8151	1.53350
$330$	−0.270335	−0.0148815
$331$	−0.972305	−0.0534427	−0.0267214	−	0.999643i	$-0.508507\pi$
$331$	−0.972305	−0.0534427	−0.0267214	+	0.999643i	$0.508507\pi$
$332$	0.259757	0.0142560
$333$	6.97568	0.382265
$334$	20.6892	1.13206
$335$	0.242779	0.0132644
$336$	−16.9278	−0.923485
$337$	−15.6764	−0.853948	−0.426974	−	0.904264i	$-0.640420\pi$
$337$	−15.6764	−0.853948	−0.426974	+	0.904264i	$0.640420\pi$
$338$	3.24208	0.176346
$339$	3.04388	0.165321
$340$	1.56425	0.0848333
$341$	−0.731830	−0.0396308
$342$	−5.50268	−0.297551
$343$	4.21547	0.227614
$344$	25.5102	1.37542
$345$	0.564555	0.0303946
$346$	16.7223	0.898995
$347$	5.58998	0.300086	0.150043	−	0.988679i	$-0.452059\pi$
$347$	5.58998	0.300086	0.150043	+	0.988679i	$0.452059\pi$
$348$	0.477741	0.0256096
$349$	33.6449	1.80097	0.900486	−	0.434885i	$-0.143211\pi$
$349$	33.6449	1.80097	0.900486	+	0.434885i	$0.143211\pi$
$350$	−26.3866	−1.41042
$351$	3.30762	0.176548
$352$	−0.805768	−0.0429476
$353$	21.3181	1.13465	0.567324	−	0.823494i	$-0.307979\pi$
$353$	21.3181	1.13465	0.567324	+	0.823494i	$0.307979\pi$
$354$	−16.7025	−0.887728
$355$	−4.17562	−0.221619
$356$	4.79618	0.254197
$357$	20.7682	1.09917
$358$	13.7450	0.726447
$359$	−25.5778	−1.34995	−0.674973	−	0.737842i	$-0.735845\pi$
$359$	−25.5778	−1.34995	−0.674973	+	0.737842i	$0.735845\pi$
$360$	1.35277	0.0712970
$361$	−6.77939	−0.356810
$362$	−5.03427	−0.264595
$363$	10.9075	0.572493
$364$	5.65847	0.296584
$365$	5.28858	0.276817
$366$	−15.3470	−0.802202
$367$	22.6777	1.18377	0.591884	−	0.806023i	$-0.298384\pi$
$367$	22.6777	1.18377	0.591884	+	0.806023i	$0.298384\pi$
$368$	4.72725	0.246425
$369$	0.962917	0.0501275
$370$	−6.19898	−0.322270
$371$	−24.3905	−1.26629
$372$	−1.14930	−0.0595884
$373$	17.7524	0.919186	0.459593	−	0.888130i	$-0.347995\pi$
$373$	17.7524	0.919186	0.459593	+	0.888130i	$0.347995\pi$
$374$	2.77718	0.143605
$375$	5.46561	0.282243
$376$	−18.6126	−0.959869
$377$	3.30762	0.170351
$378$	−5.63662	−0.289917
$379$	−3.01747	−0.154997	−0.0774986	−	0.996992i	$-0.524693\pi$
$379$	−3.01747	−0.154997	−0.0774986	+	0.996992i	$0.524693\pi$
$380$	0.942855	0.0483674
$381$	6.50048	0.333030
$382$	−1.49349	−0.0764134
$383$	−25.4068	−1.29823	−0.649113	−	0.760692i	$-0.724860\pi$
$383$	−25.4068	−1.29823	−0.649113	+	0.760692i	$0.724860\pi$
$384$	13.6167	0.694877
$385$	0.614987	0.0313427
$386$	−2.24925	−0.114484
$387$	10.6463	0.541180
$388$	2.07307	0.105244
$389$	29.0382	1.47229	0.736147	−	0.676822i	$-0.236643\pi$
$389$	29.0382	1.47229	0.736147	+	0.676822i	$0.236643\pi$
$390$	−2.93934	−0.148839
$391$	−5.79972	−0.293305
$392$	13.9524	0.704700
$393$	12.3389	0.622413
$394$	9.04436	0.455648
$395$	0.743217	0.0373953
$396$	−0.145332	−0.00730320
$397$	−3.39851	−0.170566	−0.0852831	−	0.996357i	$-0.527179\pi$
$397$	−3.39851	−0.170566	−0.0852831	+	0.996357i	$0.527179\pi$
$398$	16.1384	0.808943
$399$	12.5181	0.626688
$400$	22.1295	1.10648
$401$	−18.4906	−0.923376	−0.461688	−	0.887042i	$-0.652756\pi$
$401$	−18.4906	−0.923376	−0.461688	+	0.887042i	$0.652756\pi$
$402$	0.676913	0.0337613
$403$	−7.95714	−0.396373
$404$	1.26850	0.0631100
$405$	0.564555	0.0280530
$406$	−5.63662	−0.279741
$407$	−2.12205	−0.105186
$408$	−13.8971	−0.688009
$409$	−3.37602	−0.166934	−0.0834668	−	0.996511i	$-0.526599\pi$
$409$	−3.37602	−0.166934	−0.0834668	+	0.996511i	$0.526599\pi$
$410$	−0.855703	−0.0422602
$411$	2.84962	0.140562
$412$	4.38426	0.215997
$413$	37.9966	1.86969
$414$	1.57408	0.0773620
$415$	0.306959	0.0150680
$416$	−8.76106	−0.429546
$417$	21.0327	1.02998
$418$	1.67395	0.0818757
$419$	2.65014	0.129468	0.0647339	−	0.997903i	$-0.479380\pi$
$419$	2.65014	0.129468	0.0647339	+	0.997903i	$0.479380\pi$
$420$	0.965805	0.0471265
$421$	−9.78710	−0.476994	−0.238497	−	0.971143i	$-0.576655\pi$
$421$	−9.78710	−0.476994	−0.238497	+	0.971143i	$0.576655\pi$
$422$	14.3660	0.699325
$423$	−7.76764	−0.377676
$424$	16.3210	0.792617
$425$	−27.1501	−1.31697
$426$	−11.6424	−0.564076
$427$	34.9130	1.68956
$428$	−0.714032	−0.0345140
$429$	−1.00620	−0.0485798
$430$	−9.46088	−0.456244
$431$	14.7294	0.709489	0.354745	−	0.934963i	$-0.384568\pi$
$431$	14.7294	0.709489	0.354745	+	0.934963i	$0.384568\pi$
$432$	4.72725	0.227440
$433$	10.5393	0.506486	0.253243	−	0.967403i	$-0.418503\pi$
$433$	10.5393	0.506486	0.253243	+	0.967403i	$0.418503\pi$
$434$	13.5600	0.650902
$435$	0.564555	0.0270683
$436$	−6.81528	−0.326393
$437$	−3.49580	−0.167227
$438$	14.7455	0.704569
$439$	19.9758	0.953391	0.476696	−	0.879068i	$-0.341834\pi$
$439$	19.9758	0.953391	0.476696	+	0.879068i	$0.341834\pi$
$440$	−0.411521	−0.0196185
$441$	5.82279	0.277276
$442$	30.1961	1.43628
$443$	−6.11978	−0.290760	−0.145380	−	0.989376i	$-0.546440\pi$
$443$	−6.11978	−0.290760	−0.145380	+	0.989376i	$0.546440\pi$
$444$	−3.33256	−0.158156
$445$	5.66773	0.268676
$446$	23.3861	1.10736
$447$	5.23672	0.247688
$448$	−18.9255	−0.894145
$449$	20.4303	0.964166	0.482083	−	0.876125i	$-0.339880\pi$
$449$	20.4303	0.964166	0.482083	+	0.876125i	$0.339880\pi$
$450$	7.36872	0.347365
$451$	−0.292926	−0.0137933
$452$	−1.45419	−0.0683992
$453$	5.82423	0.273646
$454$	15.1882	0.712819
$455$	6.68671	0.313478
$456$	−8.37651	−0.392266
$457$	24.6030	1.15088	0.575440	−	0.817844i	$-0.304831\pi$
$457$	24.6030	1.15088	0.575440	+	0.817844i	$0.304831\pi$
$458$	−29.6181	−1.38396
$459$	−5.79972	−0.270708
$460$	−0.269711	−0.0125753
$461$	−35.4802	−1.65248	−0.826240	−	0.563319i	$-0.809524\pi$
$461$	−35.4802	−1.65248	−0.826240	+	0.563319i	$0.809524\pi$
$462$	1.71470	0.0797750
$463$	8.55567	0.397616	0.198808	−	0.980038i	$-0.436293\pi$
$463$	8.55567	0.397616	0.198808	+	0.980038i	$0.436293\pi$
$464$	4.72725	0.219457
$465$	−1.35815	−0.0629827
$466$	37.5654	1.74018
$467$	22.4177	1.03737	0.518685	−	0.854966i	$-0.326422\pi$
$467$	22.4177	1.03737	0.518685	+	0.854966i	$0.326422\pi$
$468$	−1.58018	−0.0730440
$469$	−1.53991	−0.0711065
$470$	6.90277	0.318401
$471$	0.208492	0.00960679
$472$	−25.4255	−1.17031
$473$	−3.23867	−0.148914
$474$	2.07223	0.0951805
$475$	−16.3648	−0.750869
$476$	−9.92180	−0.454765
$477$	6.81129	0.311868
$478$	7.88411	0.360611
$479$	23.8735	1.09081	0.545404	−	0.838173i	$-0.316376\pi$
$479$	23.8735	1.09081	0.545404	+	0.838173i	$0.316376\pi$
$480$	−1.49537	−0.0682538
$481$	−23.0729	−1.05203
$482$	−28.5787	−1.30172
$483$	−3.58089	−0.162936
$484$	−5.21093	−0.236861
$485$	2.44978	0.111239
$486$	1.57408	0.0714019
$487$	−1.70780	−0.0773876	−0.0386938	−	0.999251i	$-0.512320\pi$
$487$	−1.70780	−0.0773876	−0.0386938	+	0.999251i	$0.512320\pi$
$488$	−23.3622	−1.05756
$489$	4.45218	0.201335
$490$	−5.17446	−0.233758
$491$	40.4589	1.82588	0.912942	−	0.408088i	$-0.133805\pi$
$491$	40.4589	1.82588	0.912942	+	0.408088i	$0.133805\pi$
$492$	−0.460025	−0.0207395
$493$	−5.79972	−0.261206
$494$	18.2008	0.818891
$495$	−0.171741	−0.00771920
$496$	−11.3723	−0.510633
$497$	26.4854	1.18803
$498$	0.855860	0.0383520
$499$	41.6164	1.86301	0.931503	−	0.363734i	$-0.118498\pi$
$499$	41.6164	1.86301	0.931503	+	0.363734i	$0.118498\pi$
$500$	−2.61114	−0.116774
$501$	13.1436	0.587214
$502$	8.43986	0.376689
$503$	5.46884	0.243844	0.121922	−	0.992540i	$-0.461094\pi$
$503$	5.46884	0.243844	0.121922	+	0.992540i	$0.461094\pi$
$504$	−8.58041	−0.382202
$505$	1.49900	0.0667048
$506$	−0.478847	−0.0212873
$507$	2.05966	0.0914727
$508$	−3.10554	−0.137786
$509$	−24.0063	−1.06406	−0.532031	−	0.846725i	$-0.678571\pi$
$509$	−24.0063	−1.06406	−0.532031	+	0.846725i	$0.678571\pi$
$510$	5.15396	0.228221
$511$	−33.5447	−1.48393
$512$	10.1332	0.447829
$513$	−3.49580	−0.154343
$514$	−37.2918	−1.64487
$515$	5.18097	0.228301
$516$	−5.08616	−0.223906
$517$	2.36297	0.103923
$518$	39.3193	1.72759
$519$	10.6235	0.466320
$520$	−4.47443	−0.196217
$521$	3.34407	0.146506	0.0732532	−	0.997313i	$-0.476662\pi$
$521$	3.34407	0.146506	0.0732532	+	0.997313i	$0.476662\pi$
$522$	1.57408	0.0688958
$523$	−22.8606	−0.999622	−0.499811	−	0.866134i	$-0.666597\pi$
$523$	−22.8606	−0.999622	−0.499811	+	0.866134i	$0.666597\pi$
$524$	−5.89477	−0.257514
$525$	−16.7631	−0.731604
$526$	17.7620	0.774460
$527$	13.9524	0.607776
$528$	−1.43806	−0.0625835
$529$	1.00000	0.0434783
$530$	−6.05290	−0.262921
$531$	−10.6109	−0.460475
$532$	−5.98039	−0.259283
$533$	−3.18496	−0.137956
$534$	15.8027	0.683850
$535$	−0.843784	−0.0364800
$536$	1.03044	0.0445081
$537$	8.73207	0.376817
$538$	4.34152	0.187176
$539$	−1.77133	−0.0762966
$540$	−0.269711	−0.0116065
$541$	−34.0833	−1.46536	−0.732678	−	0.680575i	$-0.761730\pi$
$541$	−34.0833	−1.46536	−0.732678	+	0.680575i	$0.761730\pi$
$542$	30.2101	1.29764
$543$	−3.19822	−0.137249
$544$	15.3620	0.658642
$545$	−8.05375	−0.344985
$546$	18.6438	0.797881
$547$	11.2499	0.481009	0.240505	−	0.970648i	$-0.422687\pi$
$547$	11.2499	0.481009	0.240505	+	0.970648i	$0.422687\pi$
$548$	−1.36138	−0.0581553
$549$	−9.74982	−0.416112
$550$	−2.24162	−0.0955828
$551$	−3.49580	−0.148926
$552$	2.39616	0.101988
$553$	−4.71412	−0.200465
$554$	−23.1372	−0.983005
$555$	−3.93815	−0.167165
$556$	−10.0482	−0.426138
$557$	26.6127	1.12762	0.563808	−	0.825906i	$-0.309336\pi$
$557$	26.6127	1.12762	0.563808	+	0.825906i	$0.309336\pi$
$558$	−3.78677	−0.160307
$559$	−35.2138	−1.48939
$560$	9.55665	0.403842
$561$	1.76431	0.0744894
$562$	−3.07750	−0.129817
$563$	37.7720	1.59190	0.795949	−	0.605364i	$-0.206972\pi$
$563$	37.7720	1.59190	0.795949	+	0.605364i	$0.206972\pi$
$564$	3.71092	0.156258
$565$	−1.71844	−0.0722953
$566$	6.29296	0.264513
$567$	−3.58089	−0.150383
$568$	−17.7228	−0.743631
$569$	−10.0520	−0.421403	−0.210701	−	0.977550i	$-0.567575\pi$
$569$	−10.0520	−0.421403	−0.210701	+	0.977550i	$0.567575\pi$
$570$	3.10657	0.130120
$571$	−24.6421	−1.03124	−0.515619	−	0.856818i	$-0.672438\pi$
$571$	−24.6421	−1.03124	−0.515619	+	0.856818i	$0.672438\pi$
$572$	0.480702	0.0200992
$573$	−0.948797	−0.0396366
$574$	5.42760	0.226544
$575$	4.68128	0.195223
$576$	5.28513	0.220214
$577$	41.6660	1.73458	0.867290	−	0.497804i	$-0.165860\pi$
$577$	41.6660	1.73458	0.867290	+	0.497804i	$0.165860\pi$
$578$	−26.1877	−1.08927
$579$	−1.42893	−0.0593842
$580$	−0.269711	−0.0111991
$581$	−1.94700	−0.0807752
$582$	6.83045	0.283131
$583$	−2.07204	−0.0858152
$584$	22.4465	0.928845
$585$	−1.86733	−0.0772047
$586$	35.1656	1.45268
$587$	−22.0589	−0.910470	−0.455235	−	0.890371i	$-0.650445\pi$
$587$	−22.0589	−0.910470	−0.455235	+	0.890371i	$0.650445\pi$
$588$	−2.78178	−0.114719
$589$	8.40984	0.346522
$590$	9.42948	0.388205
$591$	5.74579	0.236350
$592$	−32.9757	−1.35529
$593$	3.17354	0.130322	0.0651609	−	0.997875i	$-0.479244\pi$
$593$	3.17354	0.130322	0.0651609	+	0.997875i	$0.479244\pi$
$594$	−0.478847	−0.0196473
$595$	−11.7248	−0.480669
$596$	−2.50179	−0.102477
$597$	10.2525	0.419608
$598$	−5.20647	−0.212908
$599$	7.71904	0.315391	0.157696	−	0.987488i	$-0.449593\pi$
$599$	7.71904	0.315391	0.157696	+	0.987488i	$0.449593\pi$
$600$	11.2171	0.457937
$601$	−0.813402	−0.0331793	−0.0165897	−	0.999862i	$-0.505281\pi$
$601$	−0.813402	−0.0331793	−0.0165897	+	0.999862i	$0.505281\pi$
$602$	60.0090	2.44579
$603$	0.430036	0.0175124
$604$	−2.78247	−0.113217
$605$	−6.15786	−0.250353
$606$	4.17950	0.169781
$607$	−23.0518	−0.935642	−0.467821	−	0.883823i	$-0.654961\pi$
$607$	−23.0518	−0.935642	−0.467821	+	0.883823i	$0.654961\pi$
$608$	9.25951	0.375523
$609$	−3.58089	−0.145105
$610$	8.66424	0.350805
$611$	25.6924	1.03940
$612$	2.77076	0.112001
$613$	−27.8037	−1.12298	−0.561490	−	0.827483i	$-0.689772\pi$
$613$	−27.8037	−1.12298	−0.561490	+	0.827483i	$0.689772\pi$
$614$	−3.43157	−0.138487
$615$	−0.543620	−0.0219209
$616$	2.61022	0.105169
$617$	4.69117	0.188859	0.0944297	−	0.995532i	$-0.469897\pi$
$617$	4.69117	0.188859	0.0944297	+	0.995532i	$0.469897\pi$
$618$	14.4455	0.581083
$619$	−17.9545	−0.721650	−0.360825	−	0.932633i	$-0.617505\pi$
$619$	−17.9545	−0.721650	−0.360825	+	0.932633i	$0.617505\pi$
$620$	0.648843	0.0260582
$621$	1.00000	0.0401286
$622$	51.6195	2.06975
$623$	−35.9496	−1.44029
$624$	−15.6359	−0.625938
$625$	20.3208	0.812830
$626$	27.2687	1.08988
$627$	1.06345	0.0424699
$628$	−0.0996049	−0.00397467
$629$	40.4570	1.61313
$630$	3.18218	0.126781
$631$	7.31428	0.291177	0.145589	−	0.989345i	$-0.453492\pi$
$631$	7.31428	0.291177	0.145589	+	0.989345i	$0.453492\pi$
$632$	3.15447	0.125478
$633$	9.12656	0.362748
$634$	0.0290970	0.00115559
$635$	−3.66988	−0.145635
$636$	−3.25403	−0.129031
$637$	−19.2596	−0.763091
$638$	−0.478847	−0.0189577
$639$	−7.39631	−0.292593
$640$	−7.68740	−0.303871
$641$	−27.8941	−1.10175	−0.550875	−	0.834588i	$-0.685706\pi$
$641$	−27.8941	−1.10175	−0.550875	+	0.834588i	$0.685706\pi$
$642$	−2.35263	−0.0928508
$643$	−44.5773	−1.75796	−0.878978	−	0.476863i	$-0.841774\pi$
$643$	−44.5773	−1.75796	−0.878978	+	0.476863i	$0.841774\pi$
$644$	1.71074	0.0674125
$645$	−6.01040	−0.236659
$646$	−31.9140	−1.25564
$647$	−40.8547	−1.60616	−0.803082	−	0.595869i	$-0.796808\pi$
$647$	−40.8547	−1.60616	−0.803082	+	0.595869i	$0.796808\pi$
$648$	2.39616	0.0941302
$649$	3.22792	0.126707
$650$	−24.3729	−0.955985
$651$	8.61455	0.337631
$652$	−2.12699	−0.0832992
$653$	−22.7375	−0.889786	−0.444893	−	0.895584i	$-0.646758\pi$
$653$	−22.7375	−0.889786	−0.444893	+	0.895584i	$0.646758\pi$
$654$	−22.4553	−0.878073
$655$	−6.96596	−0.272183
$656$	−4.55195	−0.177724
$657$	9.36770	0.365469
$658$	−43.7833	−1.70685
$659$	23.8558	0.929290	0.464645	−	0.885497i	$-0.346182\pi$
$659$	23.8558	0.929290	0.464645	+	0.885497i	$0.346182\pi$
$660$	0.0820478	0.00319371
$661$	24.5879	0.956357	0.478178	−	0.878263i	$-0.341297\pi$
$661$	24.5879	0.956357	0.478178	+	0.878263i	$0.341297\pi$
$662$	1.53049	0.0594842
$663$	19.1833	0.745017
$664$	1.30284	0.0505600
$665$	−7.06714	−0.274052
$666$	−10.9803	−0.425478
$667$	1.00000	0.0387202
$668$	−6.27924	−0.242951
$669$	14.8570	0.574403
$670$	−0.382154	−0.0147639
$671$	2.96596	0.114500
$672$	9.48490	0.365888
$673$	24.2057	0.933062	0.466531	−	0.884505i	$-0.345504\pi$
$673$	24.2057	0.933062	0.466531	+	0.884505i	$0.345504\pi$
$674$	24.6760	0.950483
$675$	4.68128	0.180182
$676$	−0.983983	−0.0378455
$677$	−5.23168	−0.201070	−0.100535	−	0.994934i	$-0.532055\pi$
$677$	−5.23168	−0.201070	−0.100535	+	0.994934i	$0.532055\pi$
$678$	−4.79133	−0.184010
$679$	−15.5386	−0.596317
$680$	7.84567	0.300868
$681$	9.64893	0.369748
$682$	1.15196	0.0441109
$683$	−12.8189	−0.490501	−0.245251	−	0.969460i	$-0.578870\pi$
$683$	−12.8189	−0.490501	−0.245251	+	0.969460i	$0.578870\pi$
$684$	1.67008	0.0638573
$685$	−1.60877	−0.0614679
$686$	−6.63551	−0.253345
$687$	−18.8161	−0.717877
$688$	−50.3275	−1.91872
$689$	−22.5292	−0.858293
$690$	−0.888657	−0.0338306
$691$	−14.1915	−0.539872	−0.269936	−	0.962878i	$-0.587003\pi$
$691$	−14.1915	−0.539872	−0.269936	+	0.962878i	$0.587003\pi$
$692$	−5.07528	−0.192933
$693$	1.08933	0.0413803
$694$	−8.79909	−0.334009
$695$	−11.8741	−0.450411
$696$	2.39616	0.0908264
$697$	5.58465	0.211534
$698$	−52.9600	−2.00456
$699$	23.8649	0.902654
$700$	8.00844	0.302690
$701$	−16.6500	−0.628863	−0.314432	−	0.949280i	$-0.601814\pi$
$701$	−16.6500	−0.628863	−0.314432	+	0.949280i	$0.601814\pi$
$702$	−5.20647	−0.196506
$703$	24.3856	0.919719
$704$	−1.60777	−0.0605952
$705$	4.38526	0.165159
$706$	−33.5565	−1.26292
$707$	−9.50797	−0.357584
$708$	5.06927	0.190515
$709$	2.49411	0.0936683	0.0468341	−	0.998903i	$-0.485087\pi$
$709$	2.49411	0.0936683	0.0468341	+	0.998903i	$0.485087\pi$
$710$	6.57278	0.246672
$711$	1.31647	0.0493713
$712$	24.0558	0.901529
$713$	−2.40570	−0.0900942
$714$	−32.6909	−1.22343
$715$	0.568055	0.0212440
$716$	−4.17167	−0.155902
$717$	5.00870	0.187053
$718$	40.2616	1.50255
$719$	−44.1280	−1.64570	−0.822848	−	0.568261i	$-0.807616\pi$
$719$	−44.1280	−1.64570	−0.822848	+	0.568261i	$0.807616\pi$
$720$	−2.66879	−0.0994599
$721$	−32.8621	−1.22385
$722$	10.6713	0.397146
$723$	−18.1557	−0.675219
$724$	1.52792	0.0567847
$725$	4.68128	0.173858
$726$	−17.1693	−0.637211
$727$	−29.7351	−1.10281	−0.551407	−	0.834237i	$-0.685909\pi$
$727$	−29.7351	−1.10281	−0.551407	+	0.834237i	$0.685909\pi$
$728$	28.3807	1.05186
$729$	1.00000	0.0370370
$730$	−8.32467	−0.308110
$731$	61.7455	2.28374
$732$	4.65788	0.172160
$733$	−25.0208	−0.924165	−0.462082	−	0.886837i	$-0.652898\pi$
$733$	−25.0208	−0.924165	−0.462082	+	0.886837i	$0.652898\pi$
$734$	−35.6967	−1.31759
$735$	−3.28728	−0.121253
$736$	−2.64875	−0.0976343
$737$	−0.130820	−0.00481881
$738$	−1.51571	−0.0557941
$739$	26.1618	0.962377	0.481188	−	0.876617i	$-0.340205\pi$
$739$	26.1618	0.962377	0.481188	+	0.876617i	$0.340205\pi$
$740$	1.88141	0.0691622
$741$	11.5628	0.424769
$742$	38.3927	1.40944
$743$	−23.5431	−0.863713	−0.431856	−	0.901942i	$-0.642141\pi$
$743$	−23.5431	−0.863713	−0.431856	+	0.901942i	$0.642141\pi$
$744$	−5.76445	−0.211335
$745$	−2.95642	−0.108315
$746$	−27.9438	−1.02310
$747$	0.543719	0.0198936
$748$	−0.842885	−0.0308189
$749$	5.35201	0.195558
$750$	−8.60333	−0.314149
$751$	−14.4143	−0.525984	−0.262992	−	0.964798i	$-0.584709\pi$
$751$	−14.4143	−0.525984	−0.262992	+	0.964798i	$0.584709\pi$
$752$	36.7196	1.33902
$753$	5.36176	0.195393
$754$	−5.20647	−0.189608
$755$	−3.28810	−0.119666
$756$	1.71074	0.0622189
$757$	−20.4397	−0.742895	−0.371447	−	0.928454i	$-0.621138\pi$
$757$	−20.4397	−0.742895	−0.371447	+	0.928454i	$0.621138\pi$
$758$	4.74975	0.172519
$759$	−0.304207	−0.0110420
$760$	4.72900	0.171539
$761$	−42.9369	−1.55646	−0.778230	−	0.627979i	$-0.783882\pi$
$761$	−42.9369	−1.55646	−0.778230	+	0.627979i	$0.783882\pi$
$762$	−10.2323	−0.370677
$763$	51.0838	1.84936
$764$	0.453279	0.0163991
$765$	3.27426	0.118381
$766$	39.9924	1.44498
$767$	35.0969	1.26728
$768$	−10.8636	−0.392008
$769$	−14.9836	−0.540321	−0.270161	−	0.962815i	$-0.587077\pi$
$769$	−14.9836	−0.540321	−0.270161	+	0.962815i	$0.587077\pi$
$770$	−0.968042	−0.0348858
$771$	−23.6911	−0.853213
$772$	0.682656	0.0245693
$773$	−0.397850	−0.0143097	−0.00715484	−	0.999974i	$-0.502277\pi$
$773$	−0.397850	−0.0143097	−0.00715484	+	0.999974i	$0.502277\pi$
$774$	−16.7581	−0.602358
$775$	−11.2617	−0.404534
$776$	10.3977	0.373256
$777$	24.9791	0.896122
$778$	−45.7085	−1.63873
$779$	3.36617	0.120605
$780$	0.892100	0.0319423
$781$	2.25001	0.0805115
$782$	9.12925	0.326461
$783$	1.00000	0.0357371
$784$	−27.5257	−0.983062
$785$	−0.117705	−0.00420107
$786$	−19.4224	−0.692774
$787$	37.9978	1.35448	0.677238	−	0.735764i	$-0.263177\pi$
$787$	37.9978	1.35448	0.677238	+	0.735764i	$0.263177\pi$
$788$	−2.74500	−0.0977865
$789$	11.2840	0.401722
$790$	−1.16989	−0.0416227
$791$	10.8998	0.387553
$792$	−0.728929	−0.0259014
$793$	32.2487	1.14518
$794$	5.34954	0.189848
$795$	−3.84535	−0.136380
$796$	−4.89805	−0.173607
$797$	−44.6701	−1.58229	−0.791147	−	0.611626i	$-0.790516\pi$
$797$	−44.6701	−1.58229	−0.791147	+	0.611626i	$0.790516\pi$
$798$	−19.7045	−0.697532
$799$	−45.0502	−1.59376
$800$	−12.3995	−0.438390
$801$	10.0393	0.354721
$802$	29.1057	1.02776
$803$	−2.84972	−0.100564
$804$	−0.205446	−0.00724551
$805$	2.02161	0.0712524
$806$	12.5252	0.441181
$807$	2.75812	0.0970906
$808$	6.36229	0.223825
$809$	−21.3059	−0.749075	−0.374538	−	0.927212i	$-0.622199\pi$
$809$	−21.3059	−0.749075	−0.374538	+	0.927212i	$0.622199\pi$
$810$	−0.888657	−0.0312242
$811$	25.5799	0.898231	0.449115	−	0.893474i	$-0.351739\pi$
$811$	25.5799	0.898231	0.449115	+	0.893474i	$0.351739\pi$
$812$	1.71074	0.0600351
$813$	19.1922	0.673100
$814$	3.34028	0.117077
$815$	−2.51350	−0.0880441
$816$	27.4167	0.959777
$817$	37.2172	1.30207
$818$	5.31414	0.185805
$819$	11.8442	0.413871
$820$	0.259709	0.00906943
$821$	−18.5104	−0.646016	−0.323008	−	0.946396i	$-0.604694\pi$
$821$	−18.5104	−0.646016	−0.323008	+	0.946396i	$0.604694\pi$
$822$	−4.48555	−0.156451
$823$	37.3907	1.30336	0.651679	−	0.758495i	$-0.274065\pi$
$823$	37.3907	1.30336	0.651679	+	0.758495i	$0.274065\pi$
$824$	21.9898	0.766051
$825$	−1.42408	−0.0495800
$826$	−59.8099	−2.08105
$827$	14.3452	0.498830	0.249415	−	0.968397i	$-0.419762\pi$
$827$	14.3452	0.498830	0.249415	+	0.968397i	$0.419762\pi$
$828$	−0.477741	−0.0166026
$829$	−24.2778	−0.843203	−0.421602	−	0.906781i	$-0.638532\pi$
$829$	−24.2778	−0.843203	−0.421602	+	0.906781i	$0.638532\pi$
$830$	−0.483180	−0.0167714
$831$	−14.6988	−0.509896
$832$	−17.4812	−0.606052
$833$	33.7706	1.17008
$834$	−33.1073	−1.14641
$835$	−7.42029	−0.256790
$836$	−0.508051	−0.0175713
$837$	−2.40570	−0.0831531
$838$	−4.17154	−0.144103
$839$	−26.1792	−0.903808	−0.451904	−	0.892067i	$-0.649255\pi$
$839$	−26.1792	−0.903808	−0.451904	+	0.892067i	$0.649255\pi$
$840$	4.84411	0.167138
$841$	1.00000	0.0344828
$842$	15.4057	0.530916
$843$	−1.95511	−0.0673374
$844$	−4.36013	−0.150082
$845$	−1.16279	−0.0400012
$846$	12.2269	0.420370
$847$	39.0584	1.34206
$848$	−32.1987	−1.10571
$849$	3.99785	0.137206
$850$	42.7366	1.46585
$851$	−6.97568	−0.239123
$852$	3.53351	0.121056
$853$	33.6993	1.15384	0.576922	−	0.816800i	$-0.304254\pi$
$853$	33.6993	1.15384	0.576922	+	0.816800i	$0.304254\pi$
$854$	−54.9561	−1.88056
$855$	1.97357	0.0674947
$856$	−3.58131	−0.122407
$857$	40.3546	1.37849	0.689244	−	0.724529i	$-0.257943\pi$
$857$	40.3546	1.37849	0.689244	+	0.724529i	$0.257943\pi$
$858$	1.58384	0.0540715
$859$	−10.7370	−0.366340	−0.183170	−	0.983081i	$-0.558636\pi$
$859$	−10.7370	−0.366340	−0.183170	+	0.983081i	$0.558636\pi$
$860$	2.87141	0.0979144
$861$	3.44810	0.117511
$862$	−23.1853	−0.789694
$863$	−9.43810	−0.321277	−0.160638	−	0.987013i	$-0.551355\pi$
$863$	−9.43810	−0.321277	−0.160638	+	0.987013i	$0.551355\pi$
$864$	−2.64875	−0.0901124
$865$	−5.99755	−0.203923
$866$	−16.5897	−0.563742
$867$	−16.6368	−0.565016
$868$	−4.11552	−0.139690
$869$	−0.400477	−0.0135853
$870$	−0.888657	−0.0301283
$871$	−1.42239	−0.0481960
$872$	−34.1829	−1.15758
$873$	4.33932	0.146864
$874$	5.50268	0.186131
$875$	19.5718	0.661646
$876$	−4.47533	−0.151207
$877$	5.79283	0.195610	0.0978051	−	0.995206i	$-0.468818\pi$
$877$	5.79283	0.195610	0.0978051	+	0.995206i	$0.468818\pi$
$878$	−31.4435	−1.06117
$879$	22.3404	0.753522
$880$	0.811863	0.0273679
$881$	37.3180	1.25728	0.628638	−	0.777698i	$-0.283613\pi$
$881$	37.3180	1.25728	0.628638	+	0.777698i	$0.283613\pi$
$882$	−9.16556	−0.308620
$883$	−39.7924	−1.33912	−0.669561	−	0.742757i	$-0.733518\pi$
$883$	−39.7924	−1.33912	−0.669561	+	0.742757i	$0.733518\pi$
$884$	−9.16463	−0.308240
$885$	5.99045	0.201367
$886$	9.63305	0.323629
$887$	−2.51541	−0.0844591	−0.0422296	−	0.999108i	$-0.513446\pi$
$887$	−2.51541	−0.0844591	−0.0422296	+	0.999108i	$0.513446\pi$
$888$	−16.7149	−0.560914
$889$	23.2775	0.780703
$890$	−8.92149	−0.299049
$891$	−0.304207	−0.0101913
$892$	−7.09777	−0.237651
$893$	−27.1541	−0.908678
$894$	−8.24304	−0.275689
$895$	−4.92973	−0.164783
$896$	48.7601	1.62896
$897$	−3.30762	−0.110438
$898$	−32.1590	−1.07316
$899$	−2.40570	−0.0802346
$900$	−2.23644	−0.0745479
$901$	39.5036	1.31606
$902$	0.461090	0.0153526
$903$	38.1232	1.26866
$904$	−7.29364	−0.242583
$905$	1.80557	0.0600193
$906$	−9.16783	−0.304581
$907$	9.72407	0.322882	0.161441	−	0.986882i	$-0.448386\pi$
$907$	9.72407	0.322882	0.161441	+	0.986882i	$0.448386\pi$
$908$	−4.60968	−0.152978
$909$	2.65520	0.0880673
$910$	−10.5254	−0.348915
$911$	2.39300	0.0792837	0.0396418	−	0.999214i	$-0.487378\pi$
$911$	2.39300	0.0792837	0.0396418	+	0.999214i	$0.487378\pi$
$912$	16.5255	0.547214
$913$	−0.165403	−0.00547404
$914$	−38.7272	−1.28098
$915$	5.50431	0.181967
$916$	8.98919	0.297011
$917$	44.1841	1.45909
$918$	9.12925	0.301310
$919$	−45.7955	−1.51065	−0.755327	−	0.655348i	$-0.772522\pi$
$919$	−45.7955	−1.51065	−0.755327	+	0.655348i	$0.772522\pi$
$920$	−1.35277	−0.0445994
$921$	−2.18004	−0.0718348
$922$	55.8489	1.83928
$923$	24.4642	0.805248
$924$	−0.520418	−0.0171205
$925$	−32.6551	−1.07369
$926$	−13.4673	−0.442564
$927$	9.17708	0.301415
$928$	−2.64875	−0.0869495
$929$	−46.8532	−1.53720	−0.768602	−	0.639727i	$-0.779047\pi$
$929$	−46.8532	−1.53720	−0.768602	+	0.639727i	$0.779047\pi$
$930$	2.13784	0.0701026
$931$	20.3553	0.667118
$932$	−11.4012	−0.373460
$933$	32.7933	1.07361
$934$	−35.2874	−1.15464
$935$	−0.996053	−0.0325744
$936$	−7.92560	−0.259056
$937$	38.7738	1.26669	0.633343	−	0.773871i	$-0.281682\pi$
$937$	38.7738	1.26669	0.633343	+	0.773871i	$0.281682\pi$
$938$	2.42395	0.0791448
$939$	17.3235	0.565331
$940$	−2.09502	−0.0683319
$941$	25.1648	0.820350	0.410175	−	0.912007i	$-0.365468\pi$
$941$	25.1648	0.820350	0.410175	+	0.912007i	$0.365468\pi$
$942$	−0.328183	−0.0106928
$943$	−0.962917	−0.0313569
$944$	50.1605	1.63258
$945$	2.02161	0.0657630
$946$	5.09793	0.165748
$947$	−39.0091	−1.26763	−0.633813	−	0.773486i	$-0.718511\pi$
$947$	−39.0091	−1.26763	−0.633813	+	0.773486i	$0.718511\pi$
$948$	−0.628929	−0.0204267
$949$	−30.9848	−1.00581
$950$	25.7596	0.835751
$951$	0.0184851	0.000599419 0
$952$	−49.7640	−1.61286
$953$	−34.5199	−1.11821	−0.559105	−	0.829097i	$-0.688855\pi$
$953$	−34.5199	−1.11821	−0.559105	+	0.829097i	$0.688855\pi$
$954$	−10.7215	−0.347123
$955$	0.535648	0.0173332
$956$	−2.39286	−0.0773906
$957$	−0.304207	−0.00983361
$958$	−37.5789	−1.21412
$959$	10.2042	0.329510
$960$	−2.98375	−0.0963000
$961$	−25.2126	−0.813310
$962$	36.3186	1.17096
$963$	−1.49460	−0.0481629
$964$	8.67373	0.279362
$965$	0.806708	0.0259688
$966$	5.63662	0.181355
$967$	60.0282	1.93038	0.965189	−	0.261555i	$-0.0842353\pi$
$967$	60.0282	1.93038	0.965189	+	0.261555i	$0.0842353\pi$
$968$	−26.1361	−0.840045
$969$	−20.2747	−0.651316
$970$	−3.85616	−0.123814
$971$	−42.4969	−1.36379	−0.681895	−	0.731450i	$-0.738844\pi$
$971$	−42.4969	−1.36379	−0.681895	+	0.731450i	$0.738844\pi$
$972$	−0.477741	−0.0153235
$973$	75.3159	2.41452
$974$	2.68821	0.0861359
$975$	−15.4839	−0.495881
$976$	46.0898	1.47530
$977$	−24.1211	−0.771702	−0.385851	−	0.922561i	$-0.626092\pi$
$977$	−24.1211	−0.771702	−0.385851	+	0.922561i	$0.626092\pi$
$978$	−7.00811	−0.224095
$979$	−3.05402	−0.0976069
$980$	1.57047	0.0501668
$981$	−14.2657	−0.455467
$982$	−63.6857	−2.03229
$983$	−39.8706	−1.27167	−0.635837	−	0.771824i	$-0.719345\pi$
$983$	−39.8706	−1.27167	−0.635837	+	0.771824i	$0.719345\pi$
$984$	−2.30731	−0.0735543
$985$	−3.24381	−0.103356
$986$	9.12925	0.290735
$987$	−27.8151	−0.885364
$988$	−5.52400	−0.175742
$989$	−10.6463	−0.338532
$990$	0.270335	0.00859182
$991$	−32.8665	−1.04404	−0.522019	−	0.852934i	$-0.674821\pi$
$991$	−32.8665	−1.04404	−0.522019	+	0.852934i	$0.674821\pi$
$992$	6.37210	0.202314
$993$	0.972305	0.0308552
$994$	−41.6902	−1.32233
$995$	−5.78812	−0.183496
$996$	−0.259757	−0.00823071
$997$	53.1473	1.68319	0.841597	−	0.540107i	$-0.181616\pi$
$997$	53.1473	1.68319	0.841597	+	0.540107i	$0.181616\pi$
$998$	−65.5077	−2.07361
$999$	−6.97568	−0.220701

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2001.2.a.m.1.4	✓	14
3.2	odd	2		6003.2.a.p.1.11		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2001.2.a.m.1.4	✓	14	1.1	even	1	trivial
6003.2.a.p.1.11		14	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 2001 = 3 \cdot 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2001.a (trivial)

\(f(q)\)	\(=\)	\(q-1.57408 q^{2} -1.00000 q^{3} +0.477741 q^{4} +0.564555 q^{5} +1.57408 q^{6} -3.58089 q^{7} +2.39616 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.57408 q^{2} -1.00000 q^{3} +0.477741 q^{4} +0.564555 q^{5} +1.57408 q^{6} -3.58089 q^{7} +2.39616 q^{8} +1.00000 q^{9} -0.888657 q^{10} -0.304207 q^{11} -0.477741 q^{12} -3.30762 q^{13} +5.63662 q^{14} -0.564555 q^{15} -4.72725 q^{16} +5.79972 q^{17} -1.57408 q^{18} +3.49580 q^{19} +0.269711 q^{20} +3.58089 q^{21} +0.478847 q^{22} -1.00000 q^{23} -2.39616 q^{24} -4.68128 q^{25} +5.20647 q^{26} -1.00000 q^{27} -1.71074 q^{28} -1.00000 q^{29} +0.888657 q^{30} +2.40570 q^{31} +2.64875 q^{32} +0.304207 q^{33} -9.12925 q^{34} -2.02161 q^{35} +0.477741 q^{36} +6.97568 q^{37} -5.50268 q^{38} +3.30762 q^{39} +1.35277 q^{40} +0.962917 q^{41} -5.63662 q^{42} +10.6463 q^{43} -0.145332 q^{44} +0.564555 q^{45} +1.57408 q^{46} -7.76764 q^{47} +4.72725 q^{48} +5.82279 q^{49} +7.36872 q^{50} -5.79972 q^{51} -1.58018 q^{52} +6.81129 q^{53} +1.57408 q^{54} -0.171741 q^{55} -8.58041 q^{56} -3.49580 q^{57} +1.57408 q^{58} -10.6109 q^{59} -0.269711 q^{60} -9.74982 q^{61} -3.78677 q^{62} -3.58089 q^{63} +5.28513 q^{64} -1.86733 q^{65} -0.478847 q^{66} +0.430036 q^{67} +2.77076 q^{68} +1.00000 q^{69} +3.18218 q^{70} -7.39631 q^{71} +2.39616 q^{72} +9.36770 q^{73} -10.9803 q^{74} +4.68128 q^{75} +1.67008 q^{76} +1.08933 q^{77} -5.20647 q^{78} +1.31647 q^{79} -2.66879 q^{80} +1.00000 q^{81} -1.51571 q^{82} +0.543719 q^{83} +1.71074 q^{84} +3.27426 q^{85} -16.7581 q^{86} +1.00000 q^{87} -0.728929 q^{88} +10.0393 q^{89} -0.888657 q^{90} +11.8442 q^{91} -0.477741 q^{92} -2.40570 q^{93} +12.2269 q^{94} +1.97357 q^{95} -2.64875 q^{96} +4.33932 q^{97} -9.16556 q^{98} -0.304207 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 2 q^{2} - 14 q^{3} + 12 q^{4} - 3 q^{5} + 2 q^{6} - 3 q^{7} - 6 q^{8} + 14 q^{9}+O(q^{10}) \) 14 * q - 2 * q^2 - 14 * q^3 + 12 * q^4 - 3 * q^5 + 2 * q^6 - 3 * q^7 - 6 * q^8 + 14 * q^9	\( 14 q - 2 q^{2} - 14 q^{3} + 12 q^{4} - 3 q^{5} + 2 q^{6} - 3 q^{7} - 6 q^{8} + 14 q^{9} - 5 q^{10} - 12 q^{11} - 12 q^{12} + 13 q^{13} - 9 q^{14} + 3 q^{15} - 14 q^{17} - 2 q^{18} - 9 q^{19} - 2 q^{20} + 3 q^{21} - 9 q^{22} - 14 q^{23} + 6 q^{24} + 13 q^{25} - 16 q^{26} - 14 q^{27} + 3 q^{28} - 14 q^{29} + 5 q^{30} - 28 q^{31} - 4 q^{32} + 12 q^{33} + 14 q^{34} - 9 q^{35} + 12 q^{36} - 12 q^{37} + 2 q^{38} - 13 q^{39} - 20 q^{40} - 25 q^{41} + 9 q^{42} + 5 q^{43} - 37 q^{44} - 3 q^{45} + 2 q^{46} - 17 q^{47} + 17 q^{49} - 44 q^{50} + 14 q^{51} + 25 q^{52} - 17 q^{53} + 2 q^{54} + q^{55} - 54 q^{56} + 9 q^{57} + 2 q^{58} - 18 q^{59} + 2 q^{60} - 13 q^{61} - 8 q^{62} - 3 q^{63} + 20 q^{64} - 16 q^{65} + 9 q^{66} + 2 q^{67} - 19 q^{68} + 14 q^{69} + 14 q^{70} - 55 q^{71} - 6 q^{72} + 19 q^{73} + 4 q^{74} - 13 q^{75} - 32 q^{76} - 19 q^{77} + 16 q^{78} - 68 q^{79} - 2 q^{80} + 14 q^{81} - 12 q^{82} - 21 q^{83} - 3 q^{84} + 16 q^{85} - 22 q^{86} + 14 q^{87} - 25 q^{88} - 17 q^{89} - 5 q^{90} - 30 q^{91} - 12 q^{92} + 28 q^{93} + 16 q^{94} - 55 q^{95} + 4 q^{96} + 25 q^{97} - 31 q^{98} - 12 q^{99}+O(q^{100}) \) 14 * q - 2 * q^2 - 14 * q^3 + 12 * q^4 - 3 * q^5 + 2 * q^6 - 3 * q^7 - 6 * q^8 + 14 * q^9 - 5 * q^10 - 12 * q^11 - 12 * q^12 + 13 * q^13 - 9 * q^14 + 3 * q^15 - 14 * q^17 - 2 * q^18 - 9 * q^19 - 2 * q^20 + 3 * q^21 - 9 * q^22 - 14 * q^23 + 6 * q^24 + 13 * q^25 - 16 * q^26 - 14 * q^27 + 3 * q^28 - 14 * q^29 + 5 * q^30 - 28 * q^31 - 4 * q^32 + 12 * q^33 + 14 * q^34 - 9 * q^35 + 12 * q^36 - 12 * q^37 + 2 * q^38 - 13 * q^39 - 20 * q^40 - 25 * q^41 + 9 * q^42 + 5 * q^43 - 37 * q^44 - 3 * q^45 + 2 * q^46 - 17 * q^47 + 17 * q^49 - 44 * q^50 + 14 * q^51 + 25 * q^52 - 17 * q^53 + 2 * q^54 + q^55 - 54 * q^56 + 9 * q^57 + 2 * q^58 - 18 * q^59 + 2 * q^60 - 13 * q^61 - 8 * q^62 - 3 * q^63 + 20 * q^64 - 16 * q^65 + 9 * q^66 + 2 * q^67 - 19 * q^68 + 14 * q^69 + 14 * q^70 - 55 * q^71 - 6 * q^72 + 19 * q^73 + 4 * q^74 - 13 * q^75 - 32 * q^76 - 19 * q^77 + 16 * q^78 - 68 * q^79 - 2 * q^80 + 14 * q^81 - 12 * q^82 - 21 * q^83 - 3 * q^84 + 16 * q^85 - 22 * q^86 + 14 * q^87 - 25 * q^88 - 17 * q^89 - 5 * q^90 - 30 * q^91 - 12 * q^92 + 28 * q^93 + 16 * q^94 - 55 * q^95 + 4 * q^96 + 25 * q^97 - 31 * q^98 - 12 * q^99

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